game of thrones - Why do the Tyrells come to King's Landing?

Well, the Tyrell army comes to King's Landing

along with Tywin's army to save the city from Stannis Baratheon in the Battle of the Blackwater, at the end of ACOK.

Presumably one of the reasons they decided to help is because

the Lannisters agreed to a wedding between Margaery Tyrell and Joffrey, making her queen of the realm. There may have been other guarantees made as well; or perhaps along with the wedding come other expectations of power, for example we know that Mace wants to become hand of the king.

So many Tyrells come to King's Landing in ASOS to attend this event. Some of them, such as Mace and Loras stick around to

assist in governing/ruling the realm (for example, taking up positions on the small council, in the Kingsguard, etc),

while others return to Highgarden afterwards.